Kim Cuddington
https://ecotheory.ca
11.08.22
Kim Cuddington
https://ecotheory.ca
11.08.22
rabies is caused by a genus of bullet-shaped viruses (Lyssavirus)
different kinds, or variants, that tend to attack a certain host animal, like raccoons, skunks, or bats, any rabies variant can infect any mammal.
in the saliva of infected mammals and can be spread by: (1) bites that break the skin, (2) getting saliva from an infected animal in an open cut, sore, or other wound, and (3) getting saliva from an infected animal in the mouth, nose, or eyes
99% of cases of human rabies are caused by an infected dog bite (WHO Rabies Factsheet). There are no documented events of human to human transmission other than in the case of organ transplants.
the WHO suggests that vaccinating dogs is the most cost-effective strategy for preventing rabies in people, and reduces both human deaths and the need for post-exposure treatment (WHO Rabies Factsheet).
almost all human deaths occur in Asia and Africa, where there are free-roaming dog populations.
investment in dog vaccination accounts for less than 1.5% of the global economic burden of the disease, with considerably smaller investments for Asian and African countries (Hampson et al. 2015).
Mission Rabies, a charitable organization that vaccinates dogs in various countries, estimates that vaccinating a person against rabies can cost up to 50 times more than vaccinating a dog (Mission Rabies Blog 2021).
-India probably accounts for 36% of rabies deaths, or 18,000 - 20,000 per year (WHO Rabies in India).
baits are covered in a fishmeal-based coating to encourage consumption by raccoons, coyotes, and other animals
objective function: \(\min f(x, \zeta)\),
such that: \(h(x,\zeta)\geq0\)
under chance constraint, reformulate the inequality constraint as \(P(h(x,\zeta)\geq0)\geq p\), where \(p \in [0,1]\)
relax the problem into equivalent deterministic (i.e., use the probability density function and substitute the left hand side of the constraint with a deterministic expression)
issues with convexity and stability can mean that small changes in the actual density function could cause major changes in the optimal solution
if we assume that \(\zeta_i\) is normally distributed with mean \(d_i\) and variance \(\sigma^2_i\), we can transform the constraint for each i into \[P\left(\sum x_{ij}v_{ij}\right) \ge d_i + \sigma_i q_p,\] where \(q_p\) is the p-quantile of the standard normal distribution.
then solve as usual for a given p
Thanks to several reviewers for feedback on this work.
Especial thanks to William McAuliffe for thoughtful comments, careful proofing and for being willing to read horrible excel spreadsheets.
This work was supported by
Rethink Priorities (https://rethinkpriorities.org/)
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